Definition 3.3 (Geo-indistinguishability [1]}) 

Let \(\mathcal {X}\)  be a space of locations and let \(d_{\text{E}}(x,x^{\prime })\)  denote the Euclidean distance between \(x\in \mathcal {X}\)  and \(x^{\prime }\in \mathcal {X}\) . A randomizing mechanism \(\mathcal {R}\)  is \(\epsilon \) -geo-indistinguishable if for all \(x_1,\,x_2\in \mathcal {X}\) , and every \(y\in \mathcal {X}\) , we have
\(\mathbb {P}[\mathcal {R}(x)=y] \le e^{\epsilon d_{\text{E}}(x_1,x_2)}\,\mathbb {P}\left(\mathcal {R}(x^{\prime })=y\right)\) 

